The broad, long-term objectives of this research are the developments of statistical methods for the analysis of censored failure times and incomplete repeated measures from longitudinal cancer studies. The specific aims of this competing renewal application include: (1) investigation of efficient likelihood-based methods for semi-parametric regression models for possibly correlated failure times subject to right or interval censoring; (2) construction of rank-based inference procedures for the regression analysis of incomplete repeated measures; (3) development of statistical methods for detecting genetic linkage based on censored age-of onset phenotypes or incomplete repeated measures of a quantitative trait and for assessing genome-wide statistical significance in linkage analysis; (4) exploration of strategies for accommodating population stratification in the association analysis of censored failure time phenotypes. Some of these topics are longstanding statistical problems while others are emerging issues from current cancer studies. The proposed solutions are built on sound statistical principles. The asymptotic properties of the new estimators and test statistics will be studied rigorously with the use of counting-process martingale theory, modern empirical process theory and semi-parametric efficiency theory. Their operating characteristics in practical settings will be evaluated extensively through computer simulation. The usefulness of the proposed inference procedures will be illustrated with real medical studies, some of which are carried out at the University of North Carolina. The software implementing the new methodologies will be developed for public use. This research will not only advance the fields of longitudinal data analysis, survival analysis and statistical genetics, but will also provide valuable new tools to cancer researchers. [unreadable] [unreadable]